Michel parameter in 3-3-1 model with three lepton singlets

Abstract: We show that the mass matrix of electrically neutral gauge bosons in the recently proposed model based on SU(3)C X SU(3)_L X U(1)_X group with three lepton singlets [1] has two exact eigenvalues: a zero corresponding the photon mass and the second one equaling the mass of the imaginary component A_5\mu}. Hence the neutral non-Hermitian gauge boson X^0\mu ( defined as \sqrt{2} X^0_\mu = A'_ 4\mu- i A_5\mu) is properly determined. With extra vacuum expectation value of the Higgs field n_2, there are mixings among the Standard Model W boson and the extra charged gauge boson Y carrying lepton number 2 (bilepton) as well as among neutral gauge bosons Z, Z' and X^0. These mixings lead to very rich phenomenology of the model. The leading order of the Michel parameter ($\rho$) has quite special form requiring an equality of the vacuum expectation values in the second step of spontaneous symmetry breaking, namely, k_1=k_2.